TSTP Solution File: MGT029+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : MGT029+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:17:18 EDT 2022
% Result : Theorem 73.32s 73.58s
% Output : CNFRefutation 73.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 255 ( 112 unt; 15 typ; 0 def)
% Number of atoms : 2589 ( 744 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 6444 ( 829 ~;1203 |; 72 &;4316 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 599 ( 0 ^ 589 !; 10 ?; 599 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_efficient_producers,type,
efficient_producers: $i ).
thf(tp_environment,type,
environment: $i > $o ).
thf(tp_equilibrium,type,
equilibrium: $i > $i ).
thf(tp_first_movers,type,
first_movers: $i ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_greater_or_equal,type,
greater_or_equal: $i > $i > $o ).
thf(tp_growth_rate,type,
growth_rate: $i > $i > $i ).
thf(tp_in_environment,type,
in_environment: $i > $i > $o ).
thf(tp_sK1_E,type,
sK1_E: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i > $i ).
thf(tp_sK3_T,type,
sK3_T: $i > $i ).
thf(tp_sK4_To,type,
sK4_To: $i > $i ).
thf(tp_stable,type,
stable: $i > $o ).
thf(tp_subpopulations,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( greater_or_equal @ X @ Y )
<=> ( ( greater @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
thf(2,axiom,
! [E: $i,T1: $i,T2: $i] :
( ( ( in_environment @ E @ T1 )
& ( in_environment @ E @ T2 ) )
=> ( ( greater @ T2 @ T1 )
| ( T2 = T1 )
| ( greater @ T1 @ T2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_environment) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( greater @ X @ Y )
& ( greater @ Y @ Z ) )
=> ( greater @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
thf(4,axiom,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [T: $i] :
( ( in_environment @ E @ T )
& ( greater_or_equal @ T @ ( equilibrium @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
thf(5,axiom,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
thf(6,axiom,
! [E: $i,T: $i] :
( ( ( environment @ E )
& ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ ( equilibrium @ E ) ) )
=> ( ( ( ( growth_rate @ first_movers @ T )
= zero )
& ( ( growth_rate @ efficient_producers @ T )
= zero ) )
| ( ( greater @ ( growth_rate @ first_movers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
| ( ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6) ).
thf(7,conjecture,
! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ T ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l11) ).
thf(8,negated_conjecture,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ T ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ T ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( greater_or_equal @ X @ Y )
<=> ( ( greater @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [E: $i,T1: $i,T2: $i] :
( ( ( in_environment @ E @ T1 )
& ( in_environment @ E @ T2 ) )
=> ( ( greater @ T2 @ T1 )
| ( T2 = T1 )
| ( greater @ T1 @ T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( greater @ X @ Y )
& ( greater @ Y @ Z ) )
=> ( greater @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [T: $i] :
( ( in_environment @ E @ T )
& ( greater_or_equal @ T @ ( equilibrium @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [E: $i] :
( ( ( environment @ E )
& ( stable @ E ) )
=> ? [To: $i] :
( ( in_environment @ E @ To )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ To ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [E: $i,T: $i] :
( ( ( environment @ E )
& ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater_or_equal @ T @ ( equilibrium @ E ) ) )
=> ( ( ( ( growth_rate @ first_movers @ T )
= zero )
& ( ( growth_rate @ efficient_producers @ T )
= zero ) )
| ( ( greater @ ( growth_rate @ first_movers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
| ( ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ T ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ( ( environment @ sK1_E )
& ( stable @ sK1_E ) )
=> ? [SY18: $i] :
( ( in_environment @ sK1_E @ SY18 )
& ! [SY19: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ SY19 )
& ( greater_or_equal @ SY19 @ SY18 ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ SY19 ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ SY19 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( environment @ sK1_E )
= $true ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(18,plain,
( ( stable @ sK1_E )
= $true ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(19,plain,
( ( ? [SY18: $i] :
( ( in_environment @ sK1_E @ SY18 )
& ! [SY19: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ SY19 )
& ( greater_or_equal @ SY19 @ SY18 ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ SY19 ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ SY19 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ? [SY18: $i] :
( ( in_environment @ sK1_E @ SY18 )
& ! [SY19: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ SY19 )
& ( greater_or_equal @ SY19 @ SY18 ) )
=> ( ( greater @ ( growth_rate @ efficient_producers @ SY19 ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ SY19 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [SY18: $i] :
( ( ( greater_or_equal @ ( sK2_SY19 @ SY18 ) @ SY18 )
& ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SY18 ) )
& ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SY18 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SY18 ) ) ) ) )
| ~ ( in_environment @ sK1_E @ SY18 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( greater_or_equal @ X @ Y )
| ( X = Y )
| ( greater @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( greater_or_equal @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( greater @ X @ Y )
| ( greater_or_equal @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(23,plain,
( ( ! [E: $i,T1: $i,T2: $i] :
( ~ ( in_environment @ E @ T1 )
| ~ ( in_environment @ E @ T2 )
| ( greater @ T1 @ T2 )
| ( T2 = T1 )
| ( greater @ T2 @ T1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( greater @ X @ Y )
| ~ ( greater @ Y @ Z )
| ( greater @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(25,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ( greater_or_equal @ ( sK3_T @ E ) @ ( equilibrium @ E ) )
& ( in_environment @ E @ ( sK3_T @ E ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(26,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ! [SY20: $i] :
( ~ ( greater_or_equal @ SY20 @ ( sK4_To @ E ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ SY20 )
| ( greater @ ( growth_rate @ efficient_producers @ SY20 ) @ ( growth_rate @ first_movers @ SY20 ) ) )
& ( in_environment @ E @ ( sK4_To @ E ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(28,plain,
( ( ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ ( growth_rate @ efficient_producers @ T ) @ zero )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ first_movers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ ( growth_rate @ first_movers @ T ) @ zero ) )
& ! [E: $i,T: $i] :
( ~ ( environment @ E )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ T )
| ~ ( greater_or_equal @ T @ ( equilibrium @ E ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ T ) )
| ( ( growth_rate @ efficient_producers @ T )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ T ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(29,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ! [SY20: $i] :
( ~ ( greater_or_equal @ SY20 @ ( sK4_To @ E ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ E @ SY20 )
| ( greater @ ( growth_rate @ efficient_producers @ SY20 ) @ ( growth_rate @ first_movers @ SY20 ) ) )
& ( in_environment @ E @ ( sK4_To @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [E: $i] :
( ~ ( environment @ E )
| ~ ( stable @ E )
| ( ( greater_or_equal @ ( sK3_T @ E ) @ ( equilibrium @ E ) )
& ( in_environment @ E @ ( sK3_T @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( greater @ X @ Y )
| ~ ( greater @ Y @ Z )
| ( greater @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(32,plain,
( ( ! [E: $i,T1: $i,T2: $i] :
( ~ ( in_environment @ E @ T1 )
| ~ ( in_environment @ E @ T2 )
| ( greater @ T1 @ T2 )
| ( T2 = T1 )
| ( greater @ T2 @ T1 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( greater_or_equal @ X @ Y )
| ( X = Y )
| ( greater @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( greater_or_equal @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( greater @ X @ Y )
| ( greater_or_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(34,plain,
( ( stable @ sK1_E )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(35,plain,
( ( environment @ sK1_E )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(36,plain,
( ( ! [SY18: $i] :
( ( ( greater_or_equal @ ( sK2_SY19 @ SY18 ) @ SY18 )
& ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SY18 ) )
& ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SY18 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SY18 ) ) ) ) )
| ~ ( in_environment @ sK1_E @ SY18 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(37,plain,
( ( ! [SX0: $i] :
( ~ ( environment @ SX0 )
| ~ ( stable @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( greater_or_equal @ SX1 @ ( sK4_To @ SX0 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ ( growth_rate @ first_movers @ SX1 ) ) )
| ~ ( in_environment @ SX0 @ ( sK4_To @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(38,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY19 @ SX0 ) @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SX0 ) ) )
| ~ ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SX0 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SX0 ) ) ) ) )
| ~ ( in_environment @ sK1_E @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(39,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater_or_equal @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( greater @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [SX0: $i] :
( ~ ( environment @ SX0 )
| ~ ( stable @ SX0 )
| ~ ( ~ ( greater_or_equal @ ( sK3_T @ SX0 ) @ ( equilibrium @ SX0 ) )
| ~ ( in_environment @ SX0 @ ( sK3_T @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(42,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( greater @ SV1 @ SY21 )
| ~ ( greater @ SY21 @ SY22 )
| ( greater @ SV1 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( in_environment @ SV2 @ SY23 )
| ~ ( in_environment @ SV2 @ SY24 )
| ( greater @ SY23 @ SY24 )
| ( SY24 = SY23 )
| ( greater @ SY24 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV3: $i] :
( ( ~ ( environment @ SV3 )
| ~ ( stable @ SV3 )
| ~ ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) )
| ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) )
| ~ ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) ) )
| ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater_or_equal @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( greater @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV5: $i] :
( ( ~ ( environment @ SV5 )
| ~ ( stable @ SV5 )
| ~ ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
| ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY26: $i] :
( ~ ( greater @ SV1 @ SV6 )
| ~ ( greater @ SV6 @ SY26 )
| ( greater @ SV1 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY27: $i] :
( ~ ( in_environment @ SV2 @ SV7 )
| ~ ( in_environment @ SV2 @ SY27 )
| ( greater @ SV7 @ SY27 )
| ( SY27 = SV7 )
| ( greater @ SY27 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV3: $i] :
( ( ( ~ ( environment @ SV3 )
| ~ ( stable @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) )
| ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) )
| ~ ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater_or_equal @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( greater @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(54,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(55,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(56,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(57,plain,
! [SV5: $i] :
( ( ( ~ ( environment @ SV5 )
| ~ ( stable @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
| ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV8: $i,SV6: $i,SV1: $i] :
( ( ~ ( greater @ SV1 @ SV6 )
| ~ ( greater @ SV6 @ SV8 )
| ( greater @ SV1 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV9: $i,SV7: $i,SV2: $i] :
( ( ~ ( in_environment @ SV2 @ SV7 )
| ~ ( in_environment @ SV2 @ SV9 )
| ( greater @ SV7 @ SV9 )
| ( SV9 = SV7 )
| ( greater @ SV9 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV3: $i] :
( ( ( ~ ( environment @ SV3 ) )
= $true )
| ( ( ~ ( stable @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) )
| ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) )
| ~ ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater_or_equal @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(64,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(65,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(66,plain,
! [SV5: $i] :
( ( ( ~ ( environment @ SV5 ) )
= $true )
| ( ( ~ ( stable @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
| ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV8: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( greater @ SV1 @ SV6 )
| ~ ( greater @ SV6 @ SV8 ) )
= $true )
| ( ( greater @ SV1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV9: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ SV7 )
| ~ ( in_environment @ SV2 @ SV9 ) )
= $true )
| ( ( ( greater @ SV7 @ SV9 )
| ( SV9 = SV7 )
| ( greater @ SV9 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV3: $i] :
( ( ( environment @ SV3 )
= $false )
| ( ( ~ ( stable @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) )
| ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(72,plain,
! [SV10: $i] :
( ( ! [SY28: $i] :
( ~ ( greater_or_equal @ SV10 @ SY28 )
| ( SV10 = SY28 )
| ( greater @ SV10 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(74,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV5: $i] :
( ( ( environment @ SV5 )
= $false )
| ( ( ~ ( stable @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
| ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV8: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( greater @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( greater @ SV6 @ SV8 ) )
= $true )
| ( ( greater @ SV1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV9: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in_environment @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( in_environment @ SV2 @ SV9 ) )
= $true )
| ( ( ( greater @ SV7 @ SV9 )
| ( SV9 = SV7 )
| ( greater @ SV9 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV3: $i] :
( ( ( stable @ SV3 )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( ~ ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) )
| ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(81,plain,
! [SV4: $i] :
( ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(82,plain,
! [SV11: $i,SV10: $i] :
( ( ~ ( greater_or_equal @ SV10 @ SV11 )
| ( SV10 = SV11 )
| ( greater @ SV10 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(84,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(85,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(86,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(87,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(88,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(89,plain,
! [SV5: $i] :
( ( ( stable @ SV5 )
= $false )
| ( ( environment @ SV5 )
= $false )
| ( ( ~ ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
| ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(90,plain,
! [SV8: $i,SV6: $i,SV1: $i] :
( ( ( greater @ SV1 @ SV6 )
= $false )
| ( ( ~ ( greater @ SV6 @ SV8 ) )
= $true )
| ( ( greater @ SV1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(91,plain,
! [SV9: $i,SV7: $i,SV2: $i] :
( ( ( in_environment @ SV2 @ SV7 )
= $false )
| ( ( ~ ( in_environment @ SV2 @ SV9 ) )
= $true )
| ( ( ( greater @ SV7 @ SV9 )
| ( SV9 = SV7 )
| ( greater @ SV9 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV3: $i] :
( ( ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) )
| ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV4: $i] :
( ( ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV4: $i] :
( ( ( ~ ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero ) )
= $true )
| ( ( ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV11: $i,SV10: $i] :
( ( ( ~ ( greater_or_equal @ SV10 @ SV11 ) )
= $true )
| ( ( ( SV10 = SV11 )
| ( greater @ SV10 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater_or_equal @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(98,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(100,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(101,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
| ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) )
= $false )
| ( ( environment @ SV5 )
= $false )
| ( ( stable @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV1: $i,SV8: $i,SV6: $i] :
( ( ( greater @ SV6 @ SV8 )
= $false )
| ( ( greater @ SV1 @ SV6 )
= $false )
| ( ( greater @ SV1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV7: $i,SV9: $i,SV2: $i] :
( ( ( in_environment @ SV2 @ SV9 )
= $false )
| ( ( in_environment @ SV2 @ SV7 )
= $false )
| ( ( ( greater @ SV7 @ SV9 )
| ( SV9 = SV7 )
| ( greater @ SV9 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV3: $i] :
( ( ( ~ ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) ) )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(106,plain,
! [SV3: $i] :
( ( ( ~ ( in_environment @ SV3 @ ( sK4_To @ SV3 ) ) )
= $false )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(107,plain,
! [SV4: $i] :
( ( ( ~ ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(108,plain,
! [SV4: $i] :
( ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) ) )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(109,plain,
! [SV4: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
= $false )
| ( ( ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV11: $i,SV10: $i] :
( ( ( greater_or_equal @ SV10 @ SV11 )
= $false )
| ( ( ( SV10 = SV11 )
| ( greater @ SV10 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV12: $i] :
( ( ! [SY29: $i] :
( ( SV12 != SY29 )
| ( greater_or_equal @ SV12 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV13: $i] :
( ( ! [SY30: $i] :
( ~ ( greater @ SV13 @ SY30 )
| ( greater_or_equal @ SV13 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(116,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV5: $i] :
( ( ( ~ ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) ) )
= $false )
| ( ( environment @ SV5 )
= $false )
| ( ( stable @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(118,plain,
! [SV5: $i] :
( ( ( ~ ( in_environment @ SV5 @ ( sK3_T @ SV5 ) ) )
= $false )
| ( ( environment @ SV5 )
= $false )
| ( ( stable @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(119,plain,
! [SV2: $i,SV9: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV9 )
= $true )
| ( ( ( SV9 = SV7 )
| ( greater @ SV9 @ SV7 ) )
= $true )
| ( ( in_environment @ SV2 @ SV7 )
= $false )
| ( ( in_environment @ SV2 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV3: $i] :
( ( ( ! [SY25: $i] :
( ~ ( greater_or_equal @ SY25 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SY25 )
| ( greater @ ( growth_rate @ efficient_producers @ SY25 ) @ ( growth_rate @ first_movers @ SY25 ) ) ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(121,plain,
! [SV3: $i] :
( ( ( in_environment @ SV3 @ ( sK4_To @ SV3 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(122,plain,
! [SV4: $i] :
( ( ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(123,plain,
! [SV4: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) )
= $true )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(124,plain,
! [SV4: $i] :
( ( ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
= $false )
| ( ( ~ ( in_environment @ sK1_E @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV11: $i,SV10: $i] :
( ( ( SV10 = SV11 )
= $true )
| ( ( greater @ SV10 @ SV11 )
= $true )
| ( ( greater_or_equal @ SV10 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV14: $i,SV12: $i] :
( ( ( SV12 != SV14 )
| ( greater_or_equal @ SV12 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV15: $i,SV13: $i] :
( ( ~ ( greater @ SV13 @ SV15 )
| ( greater_or_equal @ SV13 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(128,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(129,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(130,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(131,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(132,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(133,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(134,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(135,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(136,plain,
! [SV5: $i] :
( ( ( greater_or_equal @ ( sK3_T @ SV5 ) @ ( equilibrium @ SV5 ) )
= $true )
| ( ( environment @ SV5 )
= $false )
| ( ( stable @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(137,plain,
! [SV5: $i] :
( ( ( in_environment @ SV5 @ ( sK3_T @ SV5 ) )
= $true )
| ( ( environment @ SV5 )
= $false )
| ( ( stable @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(138,plain,
! [SV2: $i,SV7: $i,SV9: $i] :
( ( ( SV9 = SV7 )
= $true )
| ( ( greater @ SV9 @ SV7 )
= $true )
| ( ( greater @ SV7 @ SV9 )
= $true )
| ( ( in_environment @ SV2 @ SV7 )
= $false )
| ( ( in_environment @ SV2 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV3: $i,SV16: $i] :
( ( ( ~ ( greater_or_equal @ SV16 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV16 )
| ( greater @ ( growth_rate @ efficient_producers @ SV16 ) @ ( growth_rate @ first_movers @ SV16 ) ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV4: $i] :
( ( ( in_environment @ sK1_E @ SV4 )
= $false )
| ( ( greater_or_equal @ ( sK2_SY19 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV4: $i] :
( ( ( in_environment @ sK1_E @ SV4 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ sK1_E @ ( sK2_SY19 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV4: $i] :
( ( ( in_environment @ sK1_E @ SV4 )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sK2_SY19 @ SV4 ) ) @ zero )
= $false )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ ( sK2_SY19 @ SV4 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV14: $i,SV12: $i] :
( ( ( ( SV12 != SV14 ) )
= $true )
| ( ( greater_or_equal @ SV12 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV15: $i,SV13: $i] :
( ( ( ~ ( greater @ SV13 @ SV15 ) )
= $true )
| ( ( greater_or_equal @ SV13 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SX1 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ first_movers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SX1 ) @ zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( environment @ SX0 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SX0 @ SX1 )
| ~ ( greater_or_equal @ SX1 @ ( equilibrium @ SX0 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SX1 ) )
| ( ( growth_rate @ efficient_producers @ SX1 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(153,plain,
! [SV3: $i,SV16: $i] :
( ( ( ~ ( greater_or_equal @ SV16 @ ( sK4_To @ SV3 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV16 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV16 ) @ ( growth_rate @ first_movers @ SV16 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV14: $i,SV12: $i] :
( ( ( SV12 = SV14 )
= $false )
| ( ( greater_or_equal @ SV12 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV15: $i,SV13: $i] :
( ( ( greater @ SV13 @ SV15 )
= $false )
| ( ( greater_or_equal @ SV13 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV17: $i] :
( ( ! [SY31: $i] :
( ~ ( environment @ SV17 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SY31 )
| ~ ( greater_or_equal @ SY31 @ ( equilibrium @ SV17 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY31 ) @ zero )
| ( ( growth_rate @ first_movers @ SY31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SY31 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV18: $i] :
( ( ! [SY32: $i] :
( ~ ( environment @ SV18 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SY32 )
| ~ ( greater_or_equal @ SY32 @ ( equilibrium @ SV18 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY32 ) @ zero )
| ( ( growth_rate @ first_movers @ SY32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV19: $i] :
( ( ! [SY33: $i] :
( ~ ( environment @ SV19 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SY33 )
| ~ ( greater_or_equal @ SY33 @ ( equilibrium @ SV19 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY33 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SY33 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SY33 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV20: $i] :
( ( ! [SY34: $i] :
( ~ ( environment @ SV20 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SY34 )
| ~ ( greater_or_equal @ SY34 @ ( equilibrium @ SV20 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SY34 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SY34 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV21: $i] :
( ( ! [SY35: $i] :
( ~ ( environment @ SV21 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SY35 )
| ~ ( greater_or_equal @ SY35 @ ( equilibrium @ SV21 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SY35 ) )
| ( ( growth_rate @ first_movers @ SY35 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SY35 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV22: $i] :
( ( ! [SY36: $i] :
( ~ ( environment @ SV22 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SY36 )
| ~ ( greater_or_equal @ SY36 @ ( equilibrium @ SV22 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SY36 ) )
| ( ( growth_rate @ first_movers @ SY36 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(162,plain,
! [SV23: $i] :
( ( ! [SY37: $i] :
( ~ ( environment @ SV23 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SY37 )
| ~ ( greater_or_equal @ SY37 @ ( equilibrium @ SV23 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SY37 ) )
| ( ( growth_rate @ efficient_producers @ SY37 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SY37 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(163,plain,
! [SV24: $i] :
( ( ! [SY38: $i] :
( ~ ( environment @ SV24 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SY38 )
| ~ ( greater_or_equal @ SY38 @ ( equilibrium @ SV24 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SY38 ) )
| ( ( growth_rate @ efficient_producers @ SY38 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV3: $i,SV16: $i] :
( ( ( ~ ( greater_or_equal @ SV16 @ ( sK4_To @ SV3 ) ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV16 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV16 ) @ ( growth_rate @ first_movers @ SV16 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV25: $i,SV17: $i] :
( ( ~ ( environment @ SV17 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 )
| ~ ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV26: $i,SV18: $i] :
( ( ~ ( environment @ SV18 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 )
| ~ ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV27: $i,SV19: $i] :
( ( ~ ( environment @ SV19 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 )
| ~ ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV28: $i,SV20: $i] :
( ( ~ ( environment @ SV20 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 )
| ~ ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) )
| ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV29: $i,SV21: $i] :
( ( ~ ( environment @ SV21 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 )
| ~ ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV30: $i,SV22: $i] :
( ( ~ ( environment @ SV22 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 )
| ~ ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV31: $i,SV23: $i] :
( ( ~ ( environment @ SV23 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 )
| ~ ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV32: $i,SV24: $i] :
( ( ~ ( environment @ SV24 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 )
| ~ ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV3: $i,SV16: $i] :
( ( ( greater_or_equal @ SV16 @ ( sK4_To @ SV3 ) )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV16 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV16 ) @ ( growth_rate @ first_movers @ SV16 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV25: $i,SV17: $i] :
( ( ( ~ ( environment @ SV17 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 )
| ~ ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV26: $i,SV18: $i] :
( ( ( ~ ( environment @ SV18 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 )
| ~ ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV27: $i,SV19: $i] :
( ( ( ~ ( environment @ SV19 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 )
| ~ ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV28: $i,SV20: $i] :
( ( ( ~ ( environment @ SV20 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 )
| ~ ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV29: $i,SV21: $i] :
( ( ( ~ ( environment @ SV21 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 )
| ~ ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(179,plain,
! [SV30: $i,SV22: $i] :
( ( ( ~ ( environment @ SV22 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 )
| ~ ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV31: $i,SV23: $i] :
( ( ( ~ ( environment @ SV23 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 )
| ~ ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV32: $i,SV24: $i] :
( ( ( ~ ( environment @ SV24 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 )
| ~ ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(182,plain,
! [SV16: $i,SV3: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV3 @ SV16 )
= $false )
| ( ( greater_or_equal @ SV16 @ ( sK4_To @ SV3 ) )
= $false )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV16 ) @ ( growth_rate @ first_movers @ SV16 ) )
= $true )
| ( ( environment @ SV3 )
= $false )
| ( ( stable @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(183,plain,
! [SV25: $i,SV17: $i] :
( ( ( ~ ( environment @ SV17 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(184,plain,
! [SV26: $i,SV18: $i] :
( ( ( ~ ( environment @ SV18 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(185,plain,
! [SV27: $i,SV19: $i] :
( ( ( ~ ( environment @ SV19 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(186,plain,
! [SV28: $i,SV20: $i] :
( ( ( ~ ( environment @ SV20 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV29: $i,SV21: $i] :
( ( ( ~ ( environment @ SV21 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV30: $i,SV22: $i] :
( ( ( ~ ( environment @ SV22 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV31: $i,SV23: $i] :
( ( ( ~ ( environment @ SV23 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(190,plain,
! [SV32: $i,SV24: $i] :
( ( ( ~ ( environment @ SV24 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV25: $i,SV17: $i] :
( ( ( ~ ( environment @ SV17 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV26: $i,SV18: $i] :
( ( ( ~ ( environment @ SV18 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV27: $i,SV19: $i] :
( ( ( ~ ( environment @ SV19 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV28: $i,SV20: $i] :
( ( ( ~ ( environment @ SV20 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV29: $i,SV21: $i] :
( ( ( ~ ( environment @ SV21 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV30: $i,SV22: $i] :
( ( ( ~ ( environment @ SV22 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV31: $i,SV23: $i] :
( ( ( ~ ( environment @ SV23 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV32: $i,SV24: $i] :
( ( ( ~ ( environment @ SV24 ) )
= $true )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV25: $i,SV17: $i] :
( ( ( environment @ SV17 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV26: $i,SV18: $i] :
( ( ( environment @ SV18 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV27: $i,SV19: $i] :
( ( ( environment @ SV19 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV28: $i,SV20: $i] :
( ( ( environment @ SV20 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV29: $i,SV21: $i] :
( ( ( environment @ SV21 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV30: $i,SV22: $i] :
( ( ( environment @ SV22 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV31: $i,SV23: $i] :
( ( ( environment @ SV23 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV32: $i,SV24: $i] :
( ( ( environment @ SV24 )
= $false )
| ( ( ~ ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 ) )
= $true )
| ( ( ~ ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(207,plain,
! [SV25: $i,SV17: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 )
= $false )
| ( ( environment @ SV17 )
= $false )
| ( ( ~ ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(208,plain,
! [SV26: $i,SV18: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 )
= $false )
| ( ( environment @ SV18 )
= $false )
| ( ( ~ ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
! [SV27: $i,SV19: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 )
= $false )
| ( ( environment @ SV19 )
= $false )
| ( ( ~ ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV28: $i,SV20: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 )
= $false )
| ( ( environment @ SV20 )
= $false )
| ( ( ~ ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) ) )
= $true )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV29: $i,SV21: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 )
= $false )
| ( ( environment @ SV21 )
= $false )
| ( ( ~ ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV30: $i,SV22: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 )
= $false )
| ( ( environment @ SV22 )
= $false )
| ( ( ~ ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV31: $i,SV23: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 )
= $false )
| ( ( environment @ SV23 )
= $false )
| ( ( ~ ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(214,plain,
! [SV32: $i,SV24: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 )
= $false )
| ( ( environment @ SV24 )
= $false )
| ( ( ~ ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) ) )
= $true )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(215,plain,
! [SV17: $i,SV25: $i] :
( ( ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) )
= $false )
| ( ( environment @ SV17 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 )
= $false )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
| ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(216,plain,
! [SV18: $i,SV26: $i] :
( ( ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) )
= $false )
| ( ( environment @ SV18 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 )
= $false )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
| ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(217,plain,
! [SV19: $i,SV27: $i] :
( ( ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) )
= $false )
| ( ( environment @ SV19 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 )
= $false )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(218,plain,
! [SV20: $i,SV28: $i] :
( ( ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) )
= $false )
| ( ( environment @ SV20 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 )
= $false )
| ( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
| ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV21: $i,SV29: $i] :
( ( ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) )
= $false )
| ( ( environment @ SV21 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 )
= $false )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
| ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV22: $i,SV30: $i] :
( ( ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) )
= $false )
| ( ( environment @ SV22 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 )
= $false )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
| ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV23: $i,SV31: $i] :
( ( ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) )
= $false )
| ( ( environment @ SV23 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 )
= $false )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
| ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(222,plain,
! [SV24: $i,SV32: $i] :
( ( ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) )
= $false )
| ( ( environment @ SV24 )
= $false )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 )
= $false )
| ( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
| ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(223,plain,
! [SV17: $i,SV25: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
= $true )
| ( ( ( ( growth_rate @ first_movers @ SV25 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 )
= $false )
| ( ( environment @ SV17 )
= $false )
| ( ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV18: $i,SV26: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
= $true )
| ( ( ( ( growth_rate @ first_movers @ SV26 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 )
= $false )
| ( ( environment @ SV18 )
= $false )
| ( ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV19: $i,SV27: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
= $true )
| ( ( ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 )
= $false )
| ( ( environment @ SV19 )
= $false )
| ( ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV20: $i,SV28: $i] :
( ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
= $true )
| ( ( ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 )
= $false )
| ( ( environment @ SV20 )
= $false )
| ( ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV21: $i,SV29: $i] :
( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
= $true )
| ( ( ( ( growth_rate @ first_movers @ SV29 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 )
= $false )
| ( ( environment @ SV21 )
= $false )
| ( ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV22: $i,SV30: $i] :
( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
= $true )
| ( ( ( ( growth_rate @ first_movers @ SV30 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 )
= $false )
| ( ( environment @ SV22 )
= $false )
| ( ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV23: $i,SV31: $i] :
( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
= $true )
| ( ( ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
| ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 )
= $false )
| ( ( environment @ SV23 )
= $false )
| ( ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV24: $i,SV32: $i] :
( ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
= $true )
| ( ( ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 )
= $false )
| ( ( environment @ SV24 )
= $false )
| ( ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV17: $i,SV25: $i] :
( ( ( ( growth_rate @ first_movers @ SV25 )
= zero )
= $true )
| ( ( greater @ ( growth_rate @ first_movers @ SV25 ) @ zero )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV25 ) @ zero )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV17 @ SV25 )
= $false )
| ( ( environment @ SV17 )
= $false )
| ( ( greater_or_equal @ SV25 @ ( equilibrium @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV18: $i,SV26: $i] :
( ( ( ( growth_rate @ first_movers @ SV26 )
= zero )
= $true )
| ( ( greater @ zero @ ( growth_rate @ efficient_producers @ SV26 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV26 ) @ zero )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV18 @ SV26 )
= $false )
| ( ( environment @ SV18 )
= $false )
| ( ( greater_or_equal @ SV26 @ ( equilibrium @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(233,plain,
! [SV19: $i,SV27: $i] :
( ( ( ( growth_rate @ efficient_producers @ SV27 )
= zero )
= $true )
| ( ( greater @ ( growth_rate @ first_movers @ SV27 ) @ zero )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV27 ) @ zero )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV19 @ SV27 )
= $false )
| ( ( environment @ SV19 )
= $false )
| ( ( greater_or_equal @ SV27 @ ( equilibrium @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(234,plain,
! [SV20: $i,SV28: $i] :
( ( ( ( growth_rate @ efficient_producers @ SV28 )
= zero )
= $true )
| ( ( greater @ zero @ ( growth_rate @ efficient_producers @ SV28 ) )
= $true )
| ( ( greater @ ( growth_rate @ efficient_producers @ SV28 ) @ zero )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV20 @ SV28 )
= $false )
| ( ( environment @ SV20 )
= $false )
| ( ( greater_or_equal @ SV28 @ ( equilibrium @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(235,plain,
! [SV21: $i,SV29: $i] :
( ( ( ( growth_rate @ first_movers @ SV29 )
= zero )
= $true )
| ( ( greater @ ( growth_rate @ first_movers @ SV29 ) @ zero )
= $true )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ SV29 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV21 @ SV29 )
= $false )
| ( ( environment @ SV21 )
= $false )
| ( ( greater_or_equal @ SV29 @ ( equilibrium @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(236,plain,
! [SV22: $i,SV30: $i] :
( ( ( ( growth_rate @ first_movers @ SV30 )
= zero )
= $true )
| ( ( greater @ zero @ ( growth_rate @ efficient_producers @ SV30 ) )
= $true )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ SV30 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV22 @ SV30 )
= $false )
| ( ( environment @ SV22 )
= $false )
| ( ( greater_or_equal @ SV30 @ ( equilibrium @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(237,plain,
! [SV23: $i,SV31: $i] :
( ( ( ( growth_rate @ efficient_producers @ SV31 )
= zero )
= $true )
| ( ( greater @ ( growth_rate @ first_movers @ SV31 ) @ zero )
= $true )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ SV31 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV23 @ SV31 )
= $false )
| ( ( environment @ SV23 )
= $false )
| ( ( greater_or_equal @ SV31 @ ( equilibrium @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(238,plain,
! [SV24: $i,SV32: $i] :
( ( ( ( growth_rate @ efficient_producers @ SV32 )
= zero )
= $true )
| ( ( greater @ zero @ ( growth_rate @ efficient_producers @ SV32 ) )
= $true )
| ( ( greater @ zero @ ( growth_rate @ first_movers @ SV32 ) )
= $true )
| ( ( subpopulations @ first_movers @ efficient_producers @ SV24 @ SV32 )
= $false )
| ( ( environment @ SV24 )
= $false )
| ( ( greater_or_equal @ SV32 @ ( equilibrium @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(239,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,238,237,236,235,234,233,232,231,182,155,154,142,141,140,138,137,136,125,121,103,35]) ).
thf(240,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT029+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:18:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 6
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.19/0.35 (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full)...............
% 73.32/73.58
% 73.32/73.58 ********************************
% 73.32/73.58 * All subproblems solved! *
% 73.32/73.58 ********************************
% 73.32/73.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:239,loop_count:0,foatp_calls:1,translation:fof_full)
% 73.32/73.62
% 73.32/73.62 %**** Beginning of derivation protocol ****
% 73.32/73.62 % SZS output start CNFRefutation
% See solution above
% 73.32/73.62
% 73.32/73.62 %**** End of derivation protocol ****
% 73.32/73.62 %**** no. of clauses in derivation: 240 ****
% 73.32/73.62 %**** clause counter: 239 ****
% 73.32/73.62
% 73.32/73.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:239,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------